Half the shows Zakkrusz mentioned above are ones I've never even heard of, but based on our discussions, I'd be willing to give them all a shot. (if I can locate them)
Bakemonogatari- Koyomi Araragi was once a vampire but is now more or less human thanks to a strange homeless man he met who is an expert in so called supernatural "oddities." Koyomi now finds himself seemingly a magnet for other supernatural events and he meets girls with various supernatural issues and tries to help them.
Darker Than Black- Season 2 is airing now in Japan, I'd start with the 1st season though which is available streaming legally from the the licensor, Funimation, on their website. It's a science fiction series where two meteors have crashed into the Earth and somehow accelerated the evolution of humanity. The show follows BK201 also known as The Reaper, an agent of the Chinese mafia and his team who wage a deadly war between psychically powered humans called Contractors behind the scenes.
Natsu no Arashi- A pretty amusing random comedy. Hajime meets Arashi the ghost of a girl who died in World War II who has the abillity to travel through time. Streaming legally at crunchyroll.com.
Needless- A rather amusing over-the-top satire of a shounen fighting series with a healthy dose of fanservice.
Umeneko no Naku Koroni- The Ushinomiya family all comes togather for a meeting on a remote island to discuss how the family wealth will be divided upon learning that their father Kinzo has a terminal illness. Once there though they are stranded due to a typhoon and people begin being murdered in gruesome and seemingly impossible ways. The family attempts to find out if the culprit is one of them or if the island's legend of the Golden Witch, Beatrice, is true.
White Album- Flashing back to Japan of the 1980s, college student Toya Fuji is dating Yuki Morikawa a rising pop idol singer. However, their relationship is seriously put to the test, as their lives take them further apart and work, family issues, and other women get in the way. Available streaming legally at Crunchyroll.com.